FOM: Bourbaki

Joseph Shoenfield wrote, Mon, 31 Aug
> In fairness, I should point out that Bourbaki's treatment of
>foundations improves somewhat in the later stages with his treatment of
>structures of mathematics. This topic has been rather neglected by
>conventinal set theorists, but I think Bourbaki's treatment of it may have
>contrubuted something (at least indirectly) to category theory as
>foundations. In any case, his contribution to my education was as least
>as great as that of any teacher whom I actually met.
> A lot of people have thought about this. Of course Eilenberg
and Cartan were in Bourbaki. If you compare these ideas with what
Eilenberg, Mac Lane, Steenrod and Cartan were doing, though, you see
the influence went the other way. Bourbaki's later theory of
structures was a response to category theory--to "le virus Sammy".
Leo Corry "Nicholas Bourbaki and the concept of mathematical
structure" (SYNTHESE 92, 1992, 31-48) quotes Bourbaki's internal news
letter ("Le Tribu") to show how this happened, and some of the
effects it had on Bourbaki's work. Bourbaki's theory of structure
is never used by Bourbaki, only given and left there. And topics
important to many Bourbaki members, which they tried to treat in the
series, had to be left out finally because they could only be handled
by category theory.
Bourbaki's ideas probably have affected some people's views
of categorical foundations. But not on the categorists themselves,
even on the specific point of foundations.
Colin